document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1008137>Question 1008137</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An insurance company has determined that in a certain region the probability of lightning striking a house in a given year is about 0.0004, and the average cost of repairs of lightning damage is $7000 per incident. The company charges $22 per year for lightning insurance.\r<BR>\n" );
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document.write( "(a) What is the company's expected value for the net income from each lightning insurance policy in one year? \r<BR>\n" );
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document.write( "(b) If the company has 100,000 lightning damage policies, what is the company's expected yearly income from lightning insurance?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #623995 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=623995\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the probability of an individual house being hit by lightning = .0004\r<BR>\n" );
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document.write( "the cost of repair to damage by lightning = 7000 on the average.\r<BR>\n" );
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document.write( "the expected cost per house is therefore .0004 * 7000 = 2.8\r<BR>\n" );
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document.write( "the insurance company charges 22 per year.\r<BR>\n" );
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document.write( "their expected value is 22 - 2.8 = 19.2 per house per year.\r<BR>\n" );
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document.write( "suppose they sell the insurance policy to 100,000 houses.\r<BR>\n" );
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document.write( "they will get revenue of  22 * 100,000 = 2,200,000.\r<BR>\n" );
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document.write( "if .0004 of those houses get hit by lightning, .0004 * 100000 = 40 houses get hit by lightning each year on the average.\r<BR>\n" );
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document.write( "their cost will be 40 * 7000 = 280,000.\r<BR>\n" );
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document.write( "their net revenue will be 2,200,000 - 280,000 = 1,920,000\r<BR>\n" );
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document.write( "divide that by 100,000 and you get a net of 19.2 per house.\r<BR>\n" );
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document.write( "numbers look good.\r<BR>\n" );
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document.write( "the company's expected income per house = 19.2.\r<BR>\n" );
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document.write( "their expected income from 100,000 houses = 1,920,000.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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